Abstract
A vertex ν in a poset is a source if its indegree is zero. Further, a vertex ν in a comparability graph G is a source if there is a transitive orientation of G in which ν is a source. We characterize sources in comparability graphs in terms of forbidden subgraphs. Certain results follow, including a brief proof of a theorem by Olariu.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. Gallai (1967) Transitiv orientierbare graphen, Acta. Math. Acad. Sci. Hungar. 18, 25–66.
P. C. Gilmore and A. J. Hoffman (1964) A characterization of comparability graphs, Can. J. Math. 16, 539–548.
J. Gimbel (1988) End vertices in interval graphs, Discrete Applied Math. 21, 257–259.
F. S. Roberts (1976) Discrete Mathematical Models, Prentice Hall, Englewood Cliffs, New Jersey.
S. Olariu (1991) On the homogeneous representation of interval graphs, J. of Graph Theory 15, 65–80.
M. C. Golumbic (1980) Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York.
Author information
Authors and Affiliations
Additional information
Communicated by D. Kelly
Rights and permissions
About this article
Cite this article
Gimbel, J. Sources in posets and comparability graphs. Order 9, 361–365 (1992). https://doi.org/10.1007/BF00420356
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00420356